I am stupid – it was that plugin that makes this problem. I deactivate it and its all good.

However on our internal website, there wasnt this plugin and it did it as well. But firstly, the Download Attachments plugin works strangely there (icons arent showing for example) and I use list instead of Shift+Enter, so I am not paying attention to it anymore – our external website is more important and there it is in good shape.

Thanks for advice.